# For what values of x is #f(x)= x^3 - 4x^2 + 5x # concave or convex?

concave

convex

To determine where f(x) is concave/convex we require to find f''(x)

We now equate f''(x) to zero to find values of x where any change from concave/convex or convex/concave may occur.

• If f''(a) > 0 , then f(x) is convex

• If f''(a) < 0 , then f(x) is concave

x = 0 is to the left and f''(0) = - 8 → concave

x = 2 is to the right and f''(2) = 4 → convex

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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